hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

Schötzau, D.; Schwab, Ch.; Wihler, T. P. (2013). hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes. Siam journal on numerical analysis, 51(3), pp. 1610-1633. Society for Industrial and Applied Mathematics 10.1137/090772034

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We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Wihler, Thomas

Subjects:

500 Science > 510 Mathematics

ISSN:

1095-7170

Publisher:

Society for Industrial and Applied Mathematics

Language:

English

Submitter:

Mario Amrein

Date Deposited:

12 Mar 2014 10:12

Last Modified:

06 Aug 2019 14:05

Publisher DOI:

10.1137/090772034

BORIS DOI:

10.7892/boris.41960

URI:

https://boris.unibe.ch/id/eprint/41960

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